Problem: What is the value of $c$ if the lines with equations $y = 8x + 2$ and $y = (2c)x - 4$ are parallel?
Solution: Two lines are parallel if and only if their slopes are equal.  The slope of a line whose equation is $y = mx + b$ is $m$.  Thus $8 = 2c \Rightarrow c = \boxed{4}$.